Question

What is sin(arcsin(x)) equal to, and what is arcsin(sin(x)) equal to?

A: sin(arcsin(x)) = x and arcsin(sin(x)) = x.
B: sin(arcsin(x)) = x and arcsin(sin(x)) = sin(x).
C: sin(arcsin(x)) = 1 and arcsin(sin(x)) = x.
D: sin(arcsin(x)) = 0 and arcsin(sin(x)) = 1.

Answer 1

sin(arcsin(x)) = x and arcsin(sin(x)) = x.

Step-by-step explanation:

sin(arcsin(x)) = x: The arcsin(x) function gives you the angle whose sine is x. Then, taking the sine of that angle will give you back x since sine and arcsine are inverse functions of each other.

arcsin(sin(x)) = x: The sin(x) function gives you the sine of angle x, and then taking the arcsin of that value will give you back x since arcsin and sin are also inverse functions of each other.